Five weeks after leading the Metropolitan Transportation Authority through the worst devastation in its history, Joseph J. Lhota, the authority’s chairman, is now seriously considering a run for New York mayor, even raising the possibility of his candidacy in a meeting with Mayor Michael R. Bloomberg on Monday.

Though Mr. Lhota’s name has been floated for weeks among the city’s chattering classes, he has come to weigh a candidacy with increasing scrutiny and is expected to decide whether to run in the next few weeks, according to several people with knowledge of his plans.

A bid would require him to resign his current post, depriving Gov. Andrew M. Cuomo of his best-known appointee and instantly shaking up the 2013 mayoral campaign.

In the weeks since Mr. Lhota was widely hailed for his management of the rapid recovery of the subway system after Hurricane Sandy, business leaders have reached out to him to gauge his interest in a possible run, including Kathryn S. Wylde, the president of the Partnership for New York City.

But former Mayor Rudolph W. Giuliani, under whom Mr. Lhota was a deputy mayor and with whom he still speaks frequently, is encouraging him to run and appears poised to take on an active role in any campaign.

And Republican county leaders in the city have been contacted by a supporter, Jake Menges, an adviser to Mr. Giuliani, requesting that they hold off on endorsing a candidate.

In a city where Democrats outnumber Republicans by more than 6 to 1, the specter of a run by Mr. Lhota, who declined to comment on his plans, has galvanized some who quietly expected the 2013 race to end a two-decade stretch without a Democratic mayor. “The M.T.A. happens to be one of the few things that was run well since Sandy,” State Senator Martin J. Golden of Brooklyn said. “I think he’d win.”

Stu Loeser, who worked on Mark Green’s mayoral campaign in 2001 and later became the press secretary for Mr. Bloomberg, said that “a credible candidate like Joe Lhota entering the race on the Republican line immediately forces Democrats to think about electability in November and quickly pushes the Democratic primary to the center.”

But even supporters concede that Mr. Lhota would face trying electoral terrain, particularly because of many voters’ long-held opinions of the transportation authority.

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While 75 percent of voters in a recent Quinnipiac poll characterized the agency’s storm response as “excellent” or “good,” a separate poll found that only 38 percent of voters approved of Mr. Lhota’s overall job performance; 45 percent disapproved. In a hypothetical mayoral race against an unnamed Democrat, Mr. Lhota lost 60 to 9.

Mr. Lhota would also need to quickly raise millions of dollars, a tall order for a bureaucratic appointee without a campaign history, even one well-known among the city’s elite political and business circles. Before joining the transportation authority, Mr. Lhota was executive vice president for the Madison Square Garden Company.

While some of Mr. Lhota’s most ardent boosters, political operatives from the Giuliani era, say he could tap into the former mayor’s still-formidable network of donors, their motives may not be entirely civic. Several probably expect to become involved in, and paid by, any campaign he runs.

There is a question of how Mr. Cuomo might respond if he were forced to refill a critical administration post, though securing Mr. Cuomo’s blessing to make a mayoral run is not believed to be a leading factor in Mr. Lhota’s thinking. Cuomo aides did not respond to messages seeking comment.

Unlike another possible Republican candidate, Adolfo Carrión Jr., a former Democrat and Bronx borough president, Mr. Lhota, as a party member, would not require the approval of a majority of the Republican county leaders for a possible run at the nomination.

The city’s Republican county chairmen said they had not reached out to Mr. Lhota, but at least some welcomed his possible entry. “There is a good level of interest and enthusiasm,” said Daniel W. Isaacs, the chairman of the New York Republican County Committee. Mr. Lhota is hardly a typical Republican. On Twitter — where Mr. Lhota has at turns weighed in on “Jersey Shore,” the Yankees, and the Tea Party — his biography once read “unabashed libertarian,” though the description has since been removed. He was quoted in Capital New York last week as saying he believed that same-sex marriage should be recognized by the federal government and that marijuana “absolutely” should be legal.

Born in the Bronx, raised on Long Island and currently living in Brooklyn, Mr. Lhota is the son of a retired New York Police Department lieutenant. His wife, Tamra, was a major fund-raiser for Mr. Giuliani when he ran for mayor. He has said that a diagnosis of lymphoma seven years ago, which he has attributed to the Sept. 11 attacks, has had a mellowing effect.

But Mr. Lhota is still given to fits of combustibility. In September, he challenged a board member at the authority to “be a man” during a heated debate over meeting schedules. And last month, he likened Mr. Bloomberg to “an idiot” in a phone call with a Cuomo administration official.

The subject: the mayor’s transportation restoration predictions after Hurricane Sandy.

A version of this article appears in print on December 5, 2012, on Page A26 of the New York edition with the headline: M.T.A. Chief Weighs Run for G.O.P. Mayoral Nomination. Order Reprints|Today's Paper|Subscribe